Decoding Thermal Measurement Equations with KD2 Pro

[carter7gindenv]

Hello, I'm working with a thermal property measurement tool (KD2 pro). The manual provide the equations used to measure temperature but I'm not sure that I understand them correctly.

Temperature during heating (equation 1)
T= m₀ + m₂t + m₃ ln(t)

Temperature during cooling (equation 2)
T= m₀ + m₂t + m₃ ln(t/[t-t_h])

thermal conductivity (k) (equation 3)
k= q/ (4πm₃ )

With (according to the manual)

T = Temperature during heating
m₀ = Ambiant temperature during heating
m₂ = Rate of background temperature drift
m₃ = Slope of a line relating temperature rise to log(°T)
t_h = Heating time
q = heat per unit length

The probe works by heating up and recording the temperature evolution.

Q1. To begin with, m2*t, what does "t" stands for? Time obviously but as t_h is already "heating time" I don't really get what it relates to. (never stated in the manual)
Q2. I understand that the real temperature is calculated as the sum of 3 parts. However they elude me.
m0 not sure what temperature it is.
m2 the rate of change in temperature, kinda akin to acceleration but again what is background temperature?
m3 the what?
I also suspect that when the manual says "m2 is the rate of background temperature drift" they are actually referring to m2*t and not just to m2. It would also make more sense because otherwise the 3 parameters are defined with m_x but would not refer to the same thing.

Deciphering the parameters would already be a big help to me in understanding the whole formula.

My apologies if the post should be in engineering but I thought that it was more physics than engineering.
I also apologies to people who thought that a '90 progressive rock band named Tool made thermal equation.

Thank you for your priceless help. In the meantime I'll try to contact the manufacturer to have more info.

Additional info : The manual can be viewed here and the equations I'm talking about are 57-58 ( I'm only using a single needle probe ).

 

[Lord Jestocost]

Maybe, chapter 3 "Fundamentals of the HP Method" in "Development and Application of the Heat Pulse Method for Soil Physical Measurements" by Hailong He et al. (Reviews of Geophysics, 2018) might be of help:
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2017RG000584

 

[carter7gindenv]

Thanks for the help. I tried it but it was a bit above my level.
On another article i found that t_h is actually the time when the heating is turned off.
t seems to be either the amount of time until heating is turned off ( because apparently writing things consistently is for kids... ) or just an amount of time.

Found 2 other article having the exact same wording. *cough* plagiarism
https://www.researchgate.net/publication/261600536_Efficiency_of_the_Needle_Probe_Test_for_Evaluation_of_Thermal_Conductivity_of_Composite_Materials_Two-Scale_Analysis, second
It would not annoy me so much if the wording was clear from the beginning.
Yhea I'm ranting but I'd love a world where scientist would present equations with the same care we ask a high-schooler.

Thank you again for your help.